论文标题
体积和宏观标量曲率
Volume and macroscopic scalar curvature
论文作者
论文摘要
我们证明了三个猜想的宏观表亲：1）在存在较低的标态曲率结合的情况下，riemannian流形的简单体积的一个猜想结合，2）猜想，即在理性上基本的歧管的猜想不承认积极标度曲率的指标，3）$ l^2 $ -BETERIAR的构成量的标量，3）较低的标态曲率结合。宏观堂兄是通过在通用封面中的$ 1 $ balls卷上限制的较低标量曲率来获得的说法。
We prove the macroscopic cousins of three conjectures: 1) a conjectural bound of the simplicial volume of a Riemannian manifold in the presence of a lower scalar curvature bound, 2) the conjecture that rationally essential manifolds do not admit metrics of positive scalar curvature, 3) a conjectural bound of $L^2$-Betti numbers of aspherical Riemannian manifolds in the presence of a lower scalar curvature bound. The macroscopic cousin is the statement one obtains by replacing a lower scalar curvature bound by an upper bound on the volumes of $1$-balls in the universal cover.
